Question

If $7x+13y=27$ and $13x+7y=33$, find $x+y$

Answer 1

$7x+13y=27....\left(i\right)$
$13x+7y=33....\left(ii\right)$

Multiplying by $13$ and $7$ in equation (i) and (ii) respectively, we get
$91x+169y=351$

$\underset{–}{\underset{-}{9}1x\underset{-}{+}49y=\underset{-}{2}31}$

$120y=120$

$y=1$

Put the value of $y$ in equation (i), we get
$7x+13\times 1=27$
$\Rightarrow 7x=27-13$
$\Rightarrow 7x=14$
$\Rightarrow x=2$
Then $x+y=2+1=3$.